1. Field of the Invention
The present invention provides a method for designing a noise shaper, and more particularly, a method for designing a noise shaper with a single loop distributed feedback delta-sigma modulator.
2. Description of the Prior Art
Delta-sigma modulators have been widely used for A/D converters and D/A converters owing to its ability of noise shaping, which can suppress quantizing noise within a signal bandwidth, and increase a signal to noise ratio, or SNR.
Please refer to FIG. 1 and FIG. 2. FIG. 1 illustrates a basic configuration diagram of a prior art delta-sigma modulator 10, while FIG. 2 illustrates a related-signal diagram of the delta-sigma modulator 10 when shaping quantizing noise. In FIG. 1, the prior art delta-sigma modulator 10 includes an integrator 12, a quantizer 14, and a differentiator 16, where the integrator 12 and the differentiator 16 are complement. Referring to FIG. 2, after the delta-sigma modulator 10 receives a signal, the integrator 12 enhances a low-frequency component of the signal. Then, the quantizer 14 quantizes the signal and adds a quantizing noise eq1(z) generated by quantizing errors. Finally, the signal is returned with the differentiator 16, and the quantizing noise within the signal bandwidth is suppressed.
As to implementations of the delta-sigma modulator 10, please refer to FIG. 3 and FIG. 4. FIG. 3 illustrates a schematic diagram of a first-order delta-sigma modulator 20, while FIG. 4 illustrates a schematic diagram of an improved first-order delta-sigma modulator 30 in comparison with the delta-sigma modulator 20. Similar to the delta-sigma modulator 10, the first-order delta-sigma modulator 20 includes an integrator 22, a quantizer 24, and a differentiator 26, where the integrator 22 and the differentiator 26 are first-order and complement. Since a large direct-current gain of the integrator 22 causes output signals overflowing, under the condition that a transfer function of the delta-sigma modulator 20 will not be changed, a subtraction part of the differentiator 26 of the delta-sigma modulator 20 in FIG. 3 is moved to the front, or the input, of the integrator 22 by means of a negative feedback method, so as to form the delta-sigma modulator 30 and improve the overflow problem.
Because the noise-shaping performance of the first-order delta-sigma modulator is degraded when transforming into a phase domain, a higher-order delta-sigma modulator is necessary for suppressing low-frequency quantizing noise. As the order of the delta-sigma modulator increases, phase noise is pushed to higher frequency. However, a high-order delta-sigma modulator is very complicated. For example, please refer to FIG. 5, which illustrates a schematic diagram of a prior art third-order delta-sigma modulator 50. The delta-sigma modulator 50 includes integrators 52, 54, 56, a quantizer 58, and a differentiator. Referring to FIG. 4 and FIG. 5, for implementing the delta-sigma modulator 50, two first-order integrators are added to the delta-sigma modulator 40, and the subtraction part of the differentiator of the delta-sigma modulator 40 is moved to the input of the delta-sigma modulator 40. Nevertheless, a first-order integrator has a 90° phase shift, so a string of three first-order integrators have a 270° phase shift, causing an unstable condition. Therefore, how to determine parameters a1, a2, and a3 of the third-order delta-sigma modulator 50 is of importance.
In the prior art, the parameters are determined by means of a try-and-error method or a successive approximation method, which wastes time and may mistake. Moreover, as the order of the delta-sigma modulator increases, the parameters of the delta-sigma modulator become more difficult to be analyzed.